matematikk.net

elipsen er gitt ved r(t)= (4cosT,2sinT)

vis at elipsen har likningen

x^2/4^2 + y^2/2^2 = 1

[tex]\vec r=[4\cos(T),\,2\sin(T)][/tex]

x = 4cos(T) og y = 2sin(T)

[tex]{x^2\over 4^2}\,+\,{y^2\over 2^2}\,=\,{4^2\cos^2(T)\over 4^2}\,+\,{4\sin^^2(T)\over 4}\,=\,{cos^2(T)\,+\,sin^2(T)}\,=\,1[/tex]

): [tex]\;{x^2\over 4^2}\,+\,{y^2\over 2^2}\,=\,1[/tex]